Analytic realization of polynomial functions by multilayer feedforward neural networks

Summary form only given. An analytic method for constructing polynomial functions by multi layer feedforward neural networks has been developed. Because the polynomials consist of multiplication operations and linear weighted summations, if the multiplier can be constructed by a neural network, any polynomial function can be represented by a neural network (a single unit already has the function of weighted summation). An attempt has been made to construct a neural network module with one hidden layer that works as a multiplier. It was shown that the multiplier can be approximated by a neural network with four hidden units, with arbitrary accuracy on a bounded closed set